The discussion revolves around determining whether a given Lagrangian, which involves a scalar field and an exponential term, contains a mass term. The context is situated within the framework of special relativity and nonlinear field theory.
The discussion is ongoing, with some participants providing insights into the implications of the nonlinear nature of the theory and suggesting a method to analyze the mass term through expansion. There is no explicit consensus, but productive lines of inquiry are being pursued.
Participants note the ambiguity in defining a mass term within nonlinear field theories and the assumption that the parameter "a" may be treated as small for analysis purposes.
Astronuc said:Is this what one intended to write, or is this given in some text?
[tex]L= \frac{1}{2} (\partial_{\mu} \Psi)(\partial^{\mu} \Psi) + e^{-{(a \Psi)}^2}[/tex]
Lecticia said:Yes, exactly this Lagrangian, where \Psi is a scalar field.
dextercioby said:Well, just one question, you have the lagrangian, what are the field eqn's ?
nrqed said:This is a nonlinear field theory so, strictly speaking, there is no clear meaning for a mass term.
But I am guessing that they want you to treat the parameter "a" as small and to do a Taylor expansion of the exponential. If you do that, you will generate a mass term.
That's my guess.